Mathematical modeling based on physics, statistics or other knowledge is essential to performance of signal encoding and decoding.
Built upon unique signal models and reconstruction algorithms, as well as random or incoherent sampling, a new class of methods promise to encode and decode one- or multi-dimensional signals with a significantly reduced amount of measured, transmitted or stored data samples, and be effective managing interference effects due to random noise and aliasing. Representative methods of the new class include compressed sensing and low-rank matrix completion.
Examples of success abound demonstrating compressed sensing and low-rank matrix completion in various applications. Theoretical analyses offer not only insights on their statistical behavior but asymptotic performance guarantees under certain conditions. For certain applications however, assessment of fidelity or reliability of a specific encoding and decoding instance, as opposed to assertion of performance in a general or statistical manner, is crucial.
A case in point is compressed sensing in diagnostic MRI application. While there are numerous examples demonstrating compressed sensing's success in accelerating MR data acquisition or improving image signal-to-noise ratio (SNR), in reading an image obtained in a specific imaging instance, it is not uncommon for one to have a lingering concern that the underlying imaging scheme might have, in a convoluted and subtle manner, obscured some diagnostically important features. Setting up compressed sensing for accelerated MR data acquisition can be a complex and poorly guided process. Compared to conventional imaging schemes that rely principally on linear operators, a compressed sensing scheme, with at its core a nonlinear operator that leverages both random sampling and a sparse model to disentangle signals from interferences, poses more challenges to gauging the level of image fidelity. This is because the scheme's response to signal, interferences and encoding/decoding parameters is difficult to grasp or interpret. Sometimes a false sense of confidence may even present, as the scheme tends to produce “clean-looking” images, with interference effects spread and with no conspicuous artifacts alerting the existence of fidelity issues. When leveraging sparse modeling in diagnostic MRI therefore, there are vital needs for imaging quality control.
Parallel MRI is a subcategory of MRI. Compressed sensing is certainly applicable. Yet owing to the multi-sensor setup, imaging physics further implies redundancy/structure in the signal. There are significant opportunities for devising and optimizing mathematical modeling and for improving imaging speed, SNR and quality.
In accordance with the present invention methods are provided that judiciously apply/manage randomness, incoherence, nonlinearity and structures involved in signal encoding or decoding. In practice, where extra data for validation or comparison is often unavailable, embodiments of the invention address vital quality control needs in sophisticated encoding and decoding with unique validations and guidance, paving the way for proper and confident deployment of new encoding and decoding in applications demanding high fidelity. In multi-sensor practice, embodiments of the invention further exploit signal structures for gains in performance of signal encoding and decoding. Embodiments are illustrated for the diagnostic MRI application, and include, for example, assessment and improvement of image quality with self-validations that can be automatically performed on any specific imaging instance itself, without necessitating additional data for validation or comparison. Embodiments illustrated also include other assessments and improvements, and parallel MRI that leverages signal structures.